Hi. What does the bold ところ mean? And why is past form だった used there? (Rather than present form である, for example)?
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ところ refers to a "place" either in a concrete or abstract manner. This means it can refer to a a point in time, a physical place, or a part or portion of something. I think you understand this. Your sentence is referring to a point in time.
Here, だった and である is just modifying the point in time being referred to. であるところ would be a "non-past point in time" while だったところ refers to a point in time in the past. I think what is confusing you is how ところ is being used. For example, if we just replace ところ with 時, it would mean almost the same thing:
学生だったところ (sounds a bit odd)
When I was a student.
学生であるところ (sounds a bit odd)
When I (am / will be) a student.
学生である and 学生だった are just modifying the noun that comes after it, which, in your case is ところ. So, だったところに would mean something along the lines of "when it was (in a certain state)".